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## Abstract

Many measurements of the snowfall rate *R* and the average mass per crystal m̄ have provided values of *R*/m̄, the number of snow crystals reaching unit area of the surface per unit time. A typical number is 1 per cm.^{2} per sec. Over a whole season's data, the flux is proportional to the snowfall rate. Specifically, two-thirds of the measurements lie within a factor two of a locus *R*/m̄ (cm.^{−2} sec^{−1}) = 1.5 R^{1,0} where *R* is in millimeters of water per hour. Thus the principal contribution to any increase in the snowfall rate is the formation of new crystals, rather than the growth of existing ones.

## Abstract

Many measurements of the snowfall rate *R* and the average mass per crystal m̄ have provided values of *R*/m̄, the number of snow crystals reaching unit area of the surface per unit time. A typical number is 1 per cm.^{2} per sec. Over a whole season's data, the flux is proportional to the snowfall rate. Specifically, two-thirds of the measurements lie within a factor two of a locus *R*/m̄ (cm.^{−2} sec^{−1}) = 1.5 R^{1,0} where *R* is in millimeters of water per hour. Thus the principal contribution to any increase in the snowfall rate is the formation of new crystals, rather than the growth of existing ones.

## Abstract

Average-size distributions for aggregate snowflakes are well represented above D = 1 mm by *N*
_{D} = *N*
_{oe}
^{−AD} where *D* is the diameter of the water drop to which the aggregate would melt. This is the same equation that Marshall and Palmer (1948) reported for rain, but for rain *N*
_{o} = 8.0 × 10^{3} m^{−3} mm^{−1} and A = 41 *R*
^{−0.21} while for snow *N*
_{o} = 3.8 × 10^{3} R^{−0.87} m^{−3} mm^{−1} and A = 25.5 *R*
^{−0.48} where *R* is in millimeters of water per hour.

The sum of the sixth powers of the (melted) particle diameters in unit volume (*Z*), the mass of snow in unit volume (*M*), and the precipitation rate (*R*) are found to be related by *Z* = 2000 *R*
^{−2.0} and *M* = 250 *R*
^{−0.90}; combining these two gives *Z* = 9.57 × 10^{−3}
*M*
^{−2.2}, with *Z* in mm^{6} m^{−3}, M in mgm m^{−3} and *R* in mm hr^{−1} of water.

The relation *Z* = 2000 R^{−2.0} is in good agreement with *Z* = 2150 R^{−1.8}, an average locus through recently reported Japanese data for aggregate flakes. The relation *Z* = 200 R^{−1.6} for snow, published earlier by the present authors, is thought to be in error due to the method of sampling used at that time. Comparing standard rain and melted-snow distributions of the same R requires that there be considerable break-up of the larger particles when snow turns to rain at the melting level. Further, to explain the observed radar-signal increase from the rain over that from the snow, a considerable increase in *R* at or below the melting level is required.

## Abstract

Average-size distributions for aggregate snowflakes are well represented above D = 1 mm by *N*
_{D} = *N*
_{oe}
^{−AD} where *D* is the diameter of the water drop to which the aggregate would melt. This is the same equation that Marshall and Palmer (1948) reported for rain, but for rain *N*
_{o} = 8.0 × 10^{3} m^{−3} mm^{−1} and A = 41 *R*
^{−0.21} while for snow *N*
_{o} = 3.8 × 10^{3} R^{−0.87} m^{−3} mm^{−1} and A = 25.5 *R*
^{−0.48} where *R* is in millimeters of water per hour.

The sum of the sixth powers of the (melted) particle diameters in unit volume (*Z*), the mass of snow in unit volume (*M*), and the precipitation rate (*R*) are found to be related by *Z* = 2000 *R*
^{−2.0} and *M* = 250 *R*
^{−0.90}; combining these two gives *Z* = 9.57 × 10^{−3}
*M*
^{−2.2}, with *Z* in mm^{6} m^{−3}, M in mgm m^{−3} and *R* in mm hr^{−1} of water.

The relation *Z* = 2000 R^{−2.0} is in good agreement with *Z* = 2150 R^{−1.8}, an average locus through recently reported Japanese data for aggregate flakes. The relation *Z* = 200 R^{−1.6} for snow, published earlier by the present authors, is thought to be in error due to the method of sampling used at that time. Comparing standard rain and melted-snow distributions of the same R requires that there be considerable break-up of the larger particles when snow turns to rain at the melting level. Further, to explain the observed radar-signal increase from the rain over that from the snow, a considerable increase in *R* at or below the melting level is required.

## Abstract

According to Rayleigh scattering theory for small spheres, back scattering is proportional to |*K*
^{2}
*Z* where *K* is the dielectric factor and *Z* is the sum of the sixth powers of the diameter *D*. For small non-spherical particles of uncertain density, a similar quantity can be used: |*K*
_{1}
^{2}
*ZS*, where *K*
_{1} is the dielectric factor for the material when reduced to unit density, and *Z* = ∑*D*
_{1}
^{6}, where *D*
_{1} is the diameter of the particle when reduced to a sphere of unit density; *S* is a shape factor which for snow remains between 1 and 1.5.

An analysis of Langille and Thain's (1951) radar observations on snow shows fairly good correlation between *Z* and the snowfall *R*, particularly when considered one day at a time. An overall *Z* = *Z*(*R*) relation for snow for all days of Langille's observations is found to agree with that previously established for rain (Marshall, Langille and Palmer, 1947). That is, equal precipitation rates *R*, whether rain or snow, give equal values of *Z*.

The transition at the melting level in the case of “continuous” rain is considered in the light of this finding. Rapid aggregation amongst the raindrops and wet snowflakes in the melting region could account for the necessary differences in size distribution between snow and rain of the same precipitation rate.

Marshall and Palmer (1949) have suggested that all size distributions for precipitation are exponential when plotted as number against diameter. Taking as a fair approximation for rain that the distribution curves belong to a single family, one may establish the particular distribution by a measurement of *R*. When this approximation is less valid, as it appears to be for snow, one may still establish the particular exponential distribution by measuring *Z* and *R* simultaneously.

## Abstract

According to Rayleigh scattering theory for small spheres, back scattering is proportional to |*K*
^{2}
*Z* where *K* is the dielectric factor and *Z* is the sum of the sixth powers of the diameter *D*. For small non-spherical particles of uncertain density, a similar quantity can be used: |*K*
_{1}
^{2}
*ZS*, where *K*
_{1} is the dielectric factor for the material when reduced to unit density, and *Z* = ∑*D*
_{1}
^{6}, where *D*
_{1} is the diameter of the particle when reduced to a sphere of unit density; *S* is a shape factor which for snow remains between 1 and 1.5.

An analysis of Langille and Thain's (1951) radar observations on snow shows fairly good correlation between *Z* and the snowfall *R*, particularly when considered one day at a time. An overall *Z* = *Z*(*R*) relation for snow for all days of Langille's observations is found to agree with that previously established for rain (Marshall, Langille and Palmer, 1947). That is, equal precipitation rates *R*, whether rain or snow, give equal values of *Z*.

The transition at the melting level in the case of “continuous” rain is considered in the light of this finding. Rapid aggregation amongst the raindrops and wet snowflakes in the melting region could account for the necessary differences in size distribution between snow and rain of the same precipitation rate.

Marshall and Palmer (1949) have suggested that all size distributions for precipitation are exponential when plotted as number against diameter. Taking as a fair approximation for rain that the distribution curves belong to a single family, one may establish the particular distribution by a measurement of *R*. When this approximation is less valid, as it appears to be for snow, one may still establish the particular exponential distribution by measuring *Z* and *R* simultaneously.

## Abstract

Precipitation particles which fall from a source aloft through a wind shear are sorted as to size, the largest particles reaching the ground closest to the generating source, the smaller particles further from it. If precipitation is assumed to form continuously in cloud, with a fixed size distribution, this sorting affects significantly the size distributions to be observed below the cloud, and so the relationship between the precipitation rate *R* and the radar scattering-parameter *Z* (which is ∑*D*
^{6}, where *D* is the diameter of a raindrop or the water drop to which a snowflake would melt, and the summation is over unit volume).

As an approximation to a small isolated shower, a horizontal generating element has been taken, of linear extent 1.6 kilometers in the direction of the wind shear. The quantities *R* and *Z* tend to be less at the ground than in the generating region, the size distributions remaining the same except for upper and lower limits of size imposed by the sorting. Several values of *R* and *Z* in the generating region have been considered, all obeying *Z* = *aR ^{b}*. The

*Z/R*data below the showers have been found to be widely scattered about a locus

*Z*=

*a′Rb′,*where a′ >

*a*and

*b*′ <

*b*. If a given

*R*is obtained at the ground on many occasions involving widely varying values of

*R*aloft, the corresponding values of

*Z*are found to differ by as much as a factor of twelve. Findings regarding an isolated shower agree with the observations of Atlas and Plank (1953).

As an approximation to “continuous” snow and rain, a regular array of snow-generating elements was considered. In this, there was one element of linear extent one mile every five miles. A size sample taken at the ground over a time interval less than a minute would then yield a discontinuous distribution, with a small range of sizes contributed by each cell. The distribution of a sample collected over several minutes would be fairly smooth and resemble that aloft except as to scale. In any case, *Z* and *R* at the ground would be reduced by a factor of approximately five, compared with the values in the generating elements. This introduces a scatter in the *Z/R* data at the ground, and a shift in the *Z/R* locus, similar to those noted for the case of an isolated shower.

## Abstract

Precipitation particles which fall from a source aloft through a wind shear are sorted as to size, the largest particles reaching the ground closest to the generating source, the smaller particles further from it. If precipitation is assumed to form continuously in cloud, with a fixed size distribution, this sorting affects significantly the size distributions to be observed below the cloud, and so the relationship between the precipitation rate *R* and the radar scattering-parameter *Z* (which is ∑*D*
^{6}, where *D* is the diameter of a raindrop or the water drop to which a snowflake would melt, and the summation is over unit volume).

As an approximation to a small isolated shower, a horizontal generating element has been taken, of linear extent 1.6 kilometers in the direction of the wind shear. The quantities *R* and *Z* tend to be less at the ground than in the generating region, the size distributions remaining the same except for upper and lower limits of size imposed by the sorting. Several values of *R* and *Z* in the generating region have been considered, all obeying *Z* = *aR ^{b}*. The

*Z/R*data below the showers have been found to be widely scattered about a locus

*Z*=

*a′Rb′,*where a′ >

*a*and

*b*′ <

*b*. If a given

*R*is obtained at the ground on many occasions involving widely varying values of

*R*aloft, the corresponding values of

*Z*are found to differ by as much as a factor of twelve. Findings regarding an isolated shower agree with the observations of Atlas and Plank (1953).

As an approximation to “continuous” snow and rain, a regular array of snow-generating elements was considered. In this, there was one element of linear extent one mile every five miles. A size sample taken at the ground over a time interval less than a minute would then yield a discontinuous distribution, with a small range of sizes contributed by each cell. The distribution of a sample collected over several minutes would be fairly smooth and resemble that aloft except as to scale. In any case, *Z* and *R* at the ground would be reduced by a factor of approximately five, compared with the values in the generating elements. This introduces a scatter in the *Z/R* data at the ground, and a shift in the *Z/R* locus, similar to those noted for the case of an isolated shower.

## Abstract

No Abstract Available

## Abstract

No Abstract Available

## Abstract

A transmissometer has been used to provide a continuous record with good time resolution of falling snow. The pulsed light, of wavelength 0.45μ, traversed a path 71 m long about 20 m above ground level A total snow amount of 160 millimeters of water (mmw) from 20 storms through the 1966-67 winter season was recorded and analyzed, Attenuation by snow was found to be proportional to rate of snowfall, with the constant of proportionality 11 (db km^{-1}) / (mmw hr^{-1}). A previous experiment by Lillesaeter yielded 18 for this constant.

The attenuation from precipitation-free air was found to increase as the relative humidity increased above about 60%. Relative humidity increase between the beginning and end of a storm could lead to an increase in "clean air" attenuation of 4-5 db km^{-1}. Lack of correction for this together with the effect of thermal fluctuations on Lillesaeter's narrower transmitted beam probably account for his higher value of the constant of proportionality.

Snow amounts for individual storms deduced from the attenuation record agreed with amounts measured by standard instruments to within a factor of 2. When depths on the ground were compared, agreement was within a factor of 1.5. Over the 20 principal storms of the season, the total snow amount from the attenuation records agreed to within 2% with the accumulation in a standard Nipher gage.

## Abstract

A transmissometer has been used to provide a continuous record with good time resolution of falling snow. The pulsed light, of wavelength 0.45μ, traversed a path 71 m long about 20 m above ground level A total snow amount of 160 millimeters of water (mmw) from 20 storms through the 1966-67 winter season was recorded and analyzed, Attenuation by snow was found to be proportional to rate of snowfall, with the constant of proportionality 11 (db km^{-1}) / (mmw hr^{-1}). A previous experiment by Lillesaeter yielded 18 for this constant.

The attenuation from precipitation-free air was found to increase as the relative humidity increased above about 60%. Relative humidity increase between the beginning and end of a storm could lead to an increase in "clean air" attenuation of 4-5 db km^{-1}. Lack of correction for this together with the effect of thermal fluctuations on Lillesaeter's narrower transmitted beam probably account for his higher value of the constant of proportionality.

Snow amounts for individual storms deduced from the attenuation record agreed with amounts measured by standard instruments to within a factor of 2. When depths on the ground were compared, agreement was within a factor of 1.5. Over the 20 principal storms of the season, the total snow amount from the attenuation records agreed to within 2% with the accumulation in a standard Nipher gage.

## Abstract

The beam of a moderately sensitive 3-centimeter radar has been kept pointed to the zenith. Height/time records of snow echoes for seven winter weeks have been correlated with analyses of standard upper-air data. The major part of the record in nearly every storm contains trail patterns, formed as the snow falls from generating cells aloft. The majority of the related generating levels occur somewhere between 11,000 and 20,000 feet, between −12 and −34 degrees Celsius. Combined data from this and a previous study show that of 24 generating levels, 16 occur in maritime polar air and 16 occur in the lowest fifth of the relevant air-mass. In all but three of the cases of the present study, the snow generation takes place in stable air. Terminal speeds, deduced from the trail patterns, are estimated to range from 1 to 6 feet per second. At the leading edge of a storm, the radar usually records snow overhead for some time before any snow falls at the radar site. Occasionally the lower edge is patterned by pendulous extensions; these “stalactites” are associated with snow falling into dry air and are probably the pattern of overturning as air, chilled by evaporation, descends. Toward the end of a storm, the records tend to lack pattern, and the height of echo tends to lower. It may be that a different precipitation mechanism is involved; on the other hand, it may be that with decreasing intensity of snow the radar is unable to see to the higher levels where pattern exists.

Observations of snow cells, together with terminal-speed evidence of aggregation at low temperatures, suggest a turbulent convective mechanism, even though the cells occur in stable air. The role of growing ice crystals, acting as a thermal source, is examined. In moist stable air, the latent heat of sublimation released by growing ice crystals may result in significant vertical development, comparable to the observed depth of snow-generating cells. Calculated updraft velocities are comparable to the terminal speeds of ice crystals or aggregates. In air containing supercooled water cloud, the “sublimational” updraft is much lower than in cloud-free air; thus, shear and turbulence could develop across a cloud boundary in the presence of growing ice crystals, and be a significant factor in their aggregation. It is suggested that cloud boundaries, along which aggregation is favored, may serve as the bases for the snow-generating cells.

## Abstract

The beam of a moderately sensitive 3-centimeter radar has been kept pointed to the zenith. Height/time records of snow echoes for seven winter weeks have been correlated with analyses of standard upper-air data. The major part of the record in nearly every storm contains trail patterns, formed as the snow falls from generating cells aloft. The majority of the related generating levels occur somewhere between 11,000 and 20,000 feet, between −12 and −34 degrees Celsius. Combined data from this and a previous study show that of 24 generating levels, 16 occur in maritime polar air and 16 occur in the lowest fifth of the relevant air-mass. In all but three of the cases of the present study, the snow generation takes place in stable air. Terminal speeds, deduced from the trail patterns, are estimated to range from 1 to 6 feet per second. At the leading edge of a storm, the radar usually records snow overhead for some time before any snow falls at the radar site. Occasionally the lower edge is patterned by pendulous extensions; these “stalactites” are associated with snow falling into dry air and are probably the pattern of overturning as air, chilled by evaporation, descends. Toward the end of a storm, the records tend to lack pattern, and the height of echo tends to lower. It may be that a different precipitation mechanism is involved; on the other hand, it may be that with decreasing intensity of snow the radar is unable to see to the higher levels where pattern exists.

Observations of snow cells, together with terminal-speed evidence of aggregation at low temperatures, suggest a turbulent convective mechanism, even though the cells occur in stable air. The role of growing ice crystals, acting as a thermal source, is examined. In moist stable air, the latent heat of sublimation released by growing ice crystals may result in significant vertical development, comparable to the observed depth of snow-generating cells. Calculated updraft velocities are comparable to the terminal speeds of ice crystals or aggregates. In air containing supercooled water cloud, the “sublimational” updraft is much lower than in cloud-free air; thus, shear and turbulence could develop across a cloud boundary in the presence of growing ice crystals, and be a significant factor in their aggregation. It is suggested that cloud boundaries, along which aggregation is favored, may serve as the bases for the snow-generating cells.

## Abstract

No Abstract Available

## Abstract

No Abstract Available

## Abstract

Vertical-section radar observations of precipitation in the winter of 1951–1952 have been related to upper-air data. On three of the 22 days, there was very little signal and practically no pattern observed. It is possible that these are cases, such as described recently by Wexler and Austin (1953), in which the snow crystals grow gradually while descending through cloud-free air, at a saturation intermediate between that of ice and water.

On the remaining 19 days, trail patterns were observed. On 13 of them, well-defined snow trails, usually with generating elements visible, were detected. Upper-air analyses showed the air aloft to be stable on these days of good pattern. On six days, the records contained only parts of trails, the whole pattern being less well-defined; the air aloft was unstable on these days. Since the well-defined patterns occur on stable days, instability is not the initiating mechanism; rather, the presence of instability confuses the pattern.

For the 13 stable days, the top of the trail echo was, on the average, near the top of a main middle cloud, the top of this cloud being defined as the height above which radiosonde data show the relative humidity to drop sharply. The average cloud-top height for these 13 days was some 1300 ft above a frontal surface, the average frontal-surface height over Montreal being about 11,000 ft.

The results of this study indicate the presence of a relatively shallow “active layer” of stratiform cloud, straddling a frontal surface, in which snow-generating elements of considerable lifetime exist.

## Abstract

Vertical-section radar observations of precipitation in the winter of 1951–1952 have been related to upper-air data. On three of the 22 days, there was very little signal and practically no pattern observed. It is possible that these are cases, such as described recently by Wexler and Austin (1953), in which the snow crystals grow gradually while descending through cloud-free air, at a saturation intermediate between that of ice and water.

On the remaining 19 days, trail patterns were observed. On 13 of them, well-defined snow trails, usually with generating elements visible, were detected. Upper-air analyses showed the air aloft to be stable on these days of good pattern. On six days, the records contained only parts of trails, the whole pattern being less well-defined; the air aloft was unstable on these days. Since the well-defined patterns occur on stable days, instability is not the initiating mechanism; rather, the presence of instability confuses the pattern.

For the 13 stable days, the top of the trail echo was, on the average, near the top of a main middle cloud, the top of this cloud being defined as the height above which radiosonde data show the relative humidity to drop sharply. The average cloud-top height for these 13 days was some 1300 ft above a frontal surface, the average frontal-surface height over Montreal being about 11,000 ft.

The results of this study indicate the presence of a relatively shallow “active layer” of stratiform cloud, straddling a frontal surface, in which snow-generating elements of considerable lifetime exist.